Dynamics, Hover Configurations, and Rotor Failure Restabilization of a Morphing Quadrotor

This is the code for the paper

Dynamics, Hover Configurations, and Rotor Failure Restabilization of a Morphing Quadrotor

Trevor Avant, Unsik Lee, Brian Katona & Kristi Morgansen, American Control Conference (ACC) 2018

code

The code is written in Mathematica (11.0) and Matlab (2018b).

dynamics (Section II)

• dynamics derivation: run mathematica/dynamics.nb
  • Note: This will output 3 text files: M.txt, h.txt, and Q.txt. The contents of these files are intended to be copied into the Matlab dynamics file dx.m. This has already been done, so it is not necessary to run the .nb file again. Additionally, running this file may take a long time.

hover configurations (Section III)

• hover recovery simulation: analysis is contained in mathematica/equilibrium_math.nb

rotor failure restabilization (Section IV)

• system overview diagrams (Figures 1 & 2): run matlab/plot/plot_overview_diagrams.m

• hover recovery simulation (Figures 3 & 4): run matlab/hover_recovery.m

• region of attraction (Figure 5): run matlab/region_of_attraction.m

  • Note: This may take awhile. As an alternative, you can go to the bottom of the file and load previous results by running the commented line: load region_of_attraction_results.mat. Then, you can generate the plot by manually running the remaining lines of region_of_attraction.m.

extras

• calculation of the thrust and torque coefficients: is explained in matlab/propeller_calculations/propeller_coefficients_calculation.m

• arm motion animations: run matlab/plot/plot_arm_motions.m

  • Note: Different motions can be generated by changing the mode variable in this file.

• dynamics tests: to test dynamics of the quadrotor for different initial conditions and/or control laws, run matlab/test_dynamics.m

notes

• Our system is poorly scaled, which makes computing an LQR gain numerically challenging. In our code, we use Matlab's lqr command, which will work for our system in versions of Matlab prior to 2019a. It does not work in later versions because Matlab changed their lqr algorithm. So, if this code is run in version 2019a or later, instead of re-running the lqr command, our code will automatically load previous LQR results from the matlab/saved_results/lqr_results.mat file.

• There is a small error in Fig. 5. Our choice of Euler angles has singularities at theta = +/- pi/2 (not phi = +/- pi/2), so the blue lines should be vertical.